// 奥数难度题库 - 巧算技巧类（151-200题）
const olympiadQuestions_part4 = [
  {
    id: 151,
    text: "小明发现一个有趣的规律：1.111111111×9=9.999999999。你能用这个规律快速计算1.111111111×18的结果吗？",
    calculation: "1.111111111×18 = 1.111111111×(9×2) = (1.111111111×9)×2 = 9.999999999×2 = 19.999999998",
    answer: 19.999999998,
    type: "巧算技巧-规律探究",
    source: "5-1.md 奥赛难度 - 循环小数倍数规律"
  },
  {
    id: 152,
    text: "小红发现：1.25×3.2×2.5=1.25×(0.8×4)×2.5=(1.25×0.8)×(4×2.5)=1×10=10。你能用同样的方法计算2.5×6.4×1.25吗？",
    calculation: "2.5×6.4×1.25 = 2.5×(0.4×16)×1.25 = (2.5×0.4)×(16×1.25) = 1×20 = 20",
    answer: 20,
    type: "巧算技巧-分解因数凑整",
    source: "5-1.md 奥赛难度 - 分解因数凑整应用"
  },
  {
    id: 153,
    text: "小华发现1.1×1.1=1.21，1.1×1.2=1.32，1.1×1.3=1.43。你能总结这个规律并计算1.1×6.78的结果吗？",
    calculation: "1.1×6.78 = 7.458（首尾为7和8，中间6+7=13，需进位）",
    answer: 7.458,
    type: "巧算技巧-规律探究",
    source: "5-1.md 奥赛难度 - 乘1.1规律三位数应用"
  },
  {
    id: 154,
    text: "小刚发现：0.5×2=1，0.25×4=1，0.125×8=1。你能用这些规律快速计算1.25×0.8吗？",
    calculation: "1.25×0.8 = (1.25×8)÷10 = 10÷10 = 1",
    answer: 1,
    type: "巧算技巧-分解因数凑整",
    source: "5-1.md 奥赛难度 - 位值变换规律"
  },
  {
    id: 155,
    text: "通过计算1÷9=0.111…，2÷9=0.222…，3÷9=0.333…，你能发现规律并计算0.777…×9吗？",
    calculation: "0.777…×9 = 7",
    answer: 7,
    type: "巧算技巧-规律探究",
    source: "5-1.md 奥赛难度 - 循环小数规律应用"
  },
  {
    id: 156,
    text: "小丽发现1.25×8=10，2.5×4=10，5×2=10。你能用这个规律快速计算25×0.4吗？",
    calculation: "25×0.4 = (5×5)×(2×0.2) = (5×2)×(5×0.2) = 10×1 = 10",
    answer: 10,
    type: "巧算技巧-分解因数凑整",
    source: "5-1.md 奥赛难度 - 位值重组规律"
  },
  {
    id: 157,
    text: "小明发现1.11×1.11=1.2321，1.111×1.111=1.234321。你能发现规律并计算1.1111×1.1111吗？",
    calculation: "1.1111×1.1111 = 1.23454321",
    answer: 1.23454321,
    type: "巧算技巧-规律探究",
    source: "5-1.md 奥赛难度 - 对称数规律应用"
  },
  {
    id: 158,
    text: "小红发现0.1666…×6=1（1÷6=0.1666…）。你能用这个规律快速计算0.1666…×12吗？",
    calculation: "0.1666…×12 = (1÷6)×12 = 2",
    answer: 2,
    type: "巧算技巧-规律探究",
    source: "5-1.md 奥赛难度 - 循环小数倍数规律"
  },
  {
    id: 159,
    text: "小华发现1.25×0.8=1，2.5×0.4=1。你能用这些规律快速计算5×0.2吗？",
    calculation: "5×0.2 = 1",
    answer: 1,
    type: "巧算技巧-分解因数凑整",
    source: "5-1.md 奥赛难度 - 基础凑整规律"
  },
  {
    id: 160,
    text: "小刚发现0.142857…×7=1（1÷7=0.142857…）。你能用这个规律快速计算0.142857…×14吗？",
    calculation: "0.142857…×14 = (1÷7)×14 = 2",
    answer: 2,
    type: "巧算技巧-规律探究",
    source: "5-1.md 奥赛难度 - 循环节规律应用"
  },
  {
    id: 161,
    text: "小丽发现1.1×1.1=1.21。你能用这个规律快速计算1.1×9.999吗？",
    calculation: "1.1×9.999 = 10.9989",
    answer: 10.9989,
    type: "巧算技巧-规律探究",
    source: "5-1.md 奥赛难度 - 乘1.1规律极限应用"
  },
  {
    id: 162,
    text: "小明发现0.090909…×11=1（1÷11=0.090909…）。你能用这个规律快速计算0.090909…×22吗？",
    calculation: "0.090909…×22 = (1÷11)×22 = 2",
    answer: 2,
    type: "巧算技巧-规律探究",
    source: "5-1.md 奥赛难度 - 十一进制循环规律应用"
  },
  {
    id: 163,
    text: "小红发现0.2×5=1，0.4×2.5=1。你能用这些规律快速计算0.8×1.25吗？",
    calculation: "0.8×1.25 = 1",
    answer: 1,
    type: "巧算技巧-分解因数凑整",
    source: "5-1.md 奥赛难度 - 互为倒数规律深化"
  },
  {
    id: 164,
    text: "小华发现1.111×1.111=1.234321。你能发现规律并计算1.11111×1.11111吗？",
    calculation: "1.11111×1.11111 = 1.2345654321",
    answer: 1.2345654321,
    type: "巧算技巧-规律探究",
    source: "5-1.md 奥赛难度 - 对称数规律五位数应用"
  },
  {
    id: 165,
    text: "小刚发现0.0555…×18=1（1÷18=0.0555…）。你能用这个规律快速计算0.0555…×36吗？",
    calculation: "0.0555…×36 = (1÷18)×36 = 2",
    answer: 2,
    type: "巧算技巧-规律探究",
    source: "5-1.md 奥赛难度 - 十八进制循环规律应用"
  },
  {
    id: 166,
    text: "小丽发现0.125×8=1。你能用这个规律快速计算1.25×80吗？",
    calculation: "1.25×80 = 100",
    answer: 100,
    type: "巧算技巧-分解因数凑整",
    source: "5-1.md 奥赛难度 - 位值放大规律应用"
  },
  {
    id: 167,
    text: "小明发现1.1×1.1=1.21。你能用这个规律快速计算1.1×4.444吗？",
    calculation: "1.1×4.444 = 4.8884",
    answer: 4.8884,
    type: "巧算技巧-规律探究",
    source: "5-1.md 奥赛难度 - 乘1.1规律重复数字应用"
  },
  {
    id: 168,
    text: "小红发现0.0588235294117647…×17=1（1÷17=0.0588235294117647…）。你能用这个规律快速计算0.0588235294117647…×34吗？",
    calculation: "0.0588235294117647…×34 = (1÷17)×34 = 2",
    answer: 2,
    type: "巧算技巧-规律探究",
    source: "5-1.md 奥赛难度 - 十七进制循环规律"
  },
  {
    id: 169,
    text: "小华发现1.25×0.8=1。你能用这个规律快速计算12.5×8吗？",
    calculation: "12.5×8 = 100",
    answer: 100,
    type: "巧算技巧-分解因数凑整",
    source: "5-1.md 奥赛难度 - 位值变换规律应用"
  },
  {
    id: 170,
    text: "小刚发现1.111×1.111=1.234321。你能用这个规律快速计算1.111111×1.111111吗？",
    calculation: "1.111111×1.111111 = 1.234567654321",
    answer: 1.234567654321,
    type: "巧算技巧-规律探究",
    source: "5-1.md 奥赛难度 - 对称数规律六位数应用"
  },
  {
    id: 171,
    text: "小丽发现0.0666…×15=1（1÷15=0.0666…）。你能用这个规律快速计算0.0666…×30吗？",
    calculation: "0.0666…×30 = (1÷15)×30 = 2",
    answer: 2,
    type: "巧算技巧-规律探究",
    source: "5-1.md 奥赛难度 - 十五进制循环规律"
  },
  {
    id: 172,
    text: "小明发现0.0625×16=1。你能用这个规律快速计算0.125×8吗？",
    calculation: "0.125×8 = 1",
    answer: 1,
    type: "巧算技巧-分解因数凑整",
    source: "5-1.md 奥赛难度 - 二进制幂次规律应用"
  },
  {
    id: 173,
    text: "小红发现1.11×1.11=1.2321。你能用这个规律快速计算1.1111×1.1111吗？",
    calculation: "1.1111×1.1111 = 1.23454321",
    answer: 1.23454321,
    type: "巧算技巧-规律探究",
    source: "5-1.md 奥赛难度 - 对称数规律四位数应用"
  },
  {
    id: 174,
    text: "小华发现0.076923…×13=1（1÷13=0.076923…）。你能用这个规律快速计算0.076923…×26吗？",
    calculation: "0.076923…×26 = (1÷13)×26 = 2",
    answer: 2,
    type: "巧算技巧-规律探究",
    source: "5-1.md 奥赛难度 - 十三进制循环规律应用"
  },
  {
    id: 175,
    text: "小刚发现1.25×8=10。你能用这个规律快速计算125×0.08吗？",
    calculation: "125×0.08 = 10",
    answer: 10,
    type: "巧算技巧-分解因数凑整",
    source: "5-1.md 奥赛难度 - 位值对称规律"
  },
  {
    id: 176,
    text: "小丽发现1.1×1.1=1.21。你能用这个规律快速计算1.1×8.88吗？",
    calculation: "1.1×8.88 = 9.768",
    answer: 9.768,
    type: "巧算技巧-规律探究",
    source: "5-1.md 奥赛难度 - 乘1.1规律多位小数应用"
  },
  {
    id: 177,
    text: "小明发现1÷12=0.08333…。你能用这个规律快速计算0.08333…×24吗？",
    calculation: "0.08333…×24 = (1÷12)×24 = 2",
    answer: 2,
    type: "巧算技巧-规律探究",
    source: "5-1.md 奥赛难度 - 十二进制循环规律"
  },
  {
    id: 178,
    text: "小红发现0.1666…×6=1。你能用这个规律快速计算0.1666…×18吗？",
    calculation: "0.1666…×18 = (1÷6)×18 = 3",
    answer: 3,
    type: "巧算技巧-规律探究",
    source: "5-1.md 奥赛难度 - 六进制循环规律应用"
  },
  {
    id: 179,
    text: "小华发现0.25×4=1。你能用这个规律快速计算2.5×40吗？",
    calculation: "2.5×40 = 100",
    answer: 100,
    type: "巧算技巧-分解因数凑整",
    source: "5-1.md 奥赛难度 - 位值放大规律深化"
  },
  {
    id: 180,
    text: "小刚发现1.111×1.111=1.234321。你能用这个规律快速计算1.111111×1.111111吗？",
    calculation: "1.111111×1.111111 = 1.234567654321",
    answer: 1.234567654321,
    type: "巧算技巧-规律探究",
    source: "5-1.md 奥赛难度 - 对称数规律六位数深化"
  },
  {
    id: 181,
    text: "小丽发现0.090909…×11=1。你能用这个规律快速计算0.090909…×33吗？",
    calculation: "0.090909…×33 = (1÷11)×33 = 3",
    answer: 3,
    type: "巧算技巧-规律探究",
    source: "5-1.md 奥赛难度 - 十一进制循环规律深化"
  },
  {
    id: 182,
    text: "小明发现0.125×8=1。你能用这个规律快速计算12.5×0.8吗？",
    calculation: "12.5×0.8 = 10",
    answer: 10,
    type: "巧算技巧-分解因数凑整",
    source: "5-1.md 奥赛难度 - 位值移动规律"
  },
  {
    id: 183,
    text: "小红发现1÷6=0.1666…。你能用这个规律快速计算0.1666…×12吗？",
    calculation: "0.1666…×12 = (1÷6)×12 = 2",
    answer: 2,
    type: "巧算技巧-规律探究",
    source: "5-1.md 奥赛难度 - 六进制循环规律"
  },
  {
    id: 184,
    text: "小华发现0.2×5=1。你能用这些规律快速计算0.4×2.5吗？",
    calculation: "0.4×2.5 = 1",
    answer: 1,
    type: "巧算技巧-分解因数凑整",
    source: "5-1.md 奥赛难度 - 互为倒数规律"
  },
  {
    id: 185,
    text: "小刚发现1.111×1.111=1.234321。你能发现规律并计算1.11111×1.11111吗？",
    calculation: "1.11111×1.11111 = 1.2345654321",
    answer: 1.2345654321,
    type: "巧算技巧-规律探究",
    source: "5-1.md 奥赛难度 - 对称数规律四位数应用"
  },
  {
    id: 186,
    text: "小丽发现0.090909…×11=1。你能用这个规律快速计算0.090909…×44吗？",
    calculation: "0.090909…×44 = (1÷11)×44 = 4",
    answer: 4,
    type: "巧算技巧-规律探究",
    source: "5-1.md 奥赛难度 - 十一进制循环规律应用"
  },
  {
    id: 187,
    text: "小明发现1.25×0.8=1。你能用这个规律快速计算5×0.2吗？",
    calculation: "5×0.2 = 1",
    answer: 1,
    type: "巧算技巧-分解因数凑整",
    source: "5-1.md 奥赛难度 - 基础凑整规律"
  },
  {
    id: 188,
    text: "小红发现1.1×1.1=1.21。你能用这个规律快速计算1.1×5.67吗？",
    calculation: "1.1×5.67 = 6.237",
    answer: 6.237,
    type: "巧算技巧-规律探究",
    source: "5-1.md 奥赛难度 - 乘1.1规律三位数应用"
  },
  {
    id: 189,
    text: "小华发现1÷12=0.08333…。你能用这个规律快速计算0.08333…×36吗？",
    calculation: "0.08333…×36 = (1÷12)×36 = 3",
    answer: 3,
    type: "巧算技巧-规律探究",
    source: "5-1.md 奥赛难度 - 十二进制循环规律"
  },
  {
    id: 190,
    text: "小刚发现0.1666…×6=1。你能用这个规律快速计算0.1666…×24吗？",
    calculation: "0.1666…×24 = (1÷6)×24 = 4",
    answer: 4,
    type: "巧算技巧-规律探究",
    source: "5-1.md 奥赛难度 - 六进制循环规律应用"
  },
  {
    id: 191,
    text: "小丽发现0.125×8=1。你能用这个规律快速计算1.25×80吗？",
    calculation: "1.25×80 = 100",
    answer: 100,
    type: "巧算技巧-分解因数凑整",
    source: "5-1.md 奥赛难度 - 位值放大规律应用"
  },
  {
    id: 192,
    text: "小明发现1.11×1.11=1.2321。你能用这个规律快速计算1.1111×1.1111吗？",
    calculation: "1.1111×1.1111 = 1.23454321",
    answer: 1.23454321,
    type: "巧算技巧-规律探究",
    source: "5-1.md 奥赛难度 - 对称数规律五位数应用"
  },
  {
    id: 193,
    text: "小红发现0.0555…×18=1。你能用这个规律快速计算0.0555…×54吗？",
    calculation: "0.0555…×54 = (1÷18)×54 = 3",
    answer: 3,
    type: "巧算技巧-规律探究",
    source: "5-1.md 奥赛难度 - 十八进制循环规律应用"
  },
  {
    id: 194,
    text: "小华发现0.0588235294117647…×17=1。你能用这个规律快速计算0.0588235294117647…×51吗？",
    calculation: "0.0588235294117647…×51 = (1÷17)×51 = 3",
    answer: 3,
    type: "巧算技巧-规律探究",
    source: "5-1.md 奥赛难度 - 十七进制循环规律"
  },
  {
    id: 195,
    text: "小刚发现1.25×0.8=1。你能用这个规律快速计算12.5×8吗？",
    calculation: "12.5×8 = 100",
    answer: 100,
    type: "巧算技巧-分解因数凑整",
    source: "5-1.md 奥赛难度 - 位值变换规律应用"
  },
  {
    id: 196,
    text: "小丽发现1.111×1.111=1.234321。你能用这个规律快速计算1.111111×1.111111吗？",
    calculation: "1.111111×1.111111 = 1.234567654321",
    answer: 1.234567654321,
    type: "巧算技巧-规律探究",
    source: "5-1.md 奥赛难度 - 对称数规律六位数应用"
  },
  {
    id: 197,
    text: "小明发现0.0666…×15=1。你能用这个规律快速计算0.0666…×45吗？",
    calculation: "0.0666…×45 = (1÷15)×45 = 3",
    answer: 3,
    type: "巧算技巧-规律探究",
    source: "5-1.md 奥赛难度 - 十五进制循环规律"
  },
  {
    id: 198,
    text: "小红发现0.0625×16=1。你能用这个规律快速计算0.125×16吗？",
    calculation: "0.125×16 = 2",
    answer: 2,
    type: "巧算技巧-分解因数凑整",
    source: "5-1.md 奥赛难度 - 二进制幂次规律应用"
  },
  {
    id: 199,
    text: "小华发现1.1×1.1=1.21。你能用这个规律快速计算1.1×4.444吗？",
    calculation: "1.1×4.444 = 4.8884",
    answer: 4.8884,
    type: "巧算技巧-规律探究",
    source: "5-1.md 奥赛难度 - 乘1.1规律重复数字应用"
  },
  {
    id: 200,
    text: "小刚发现1.11×1.11=1.2321。你能用这个规律快速计算1.1111111×1.1111111吗？",
    calculation: "1.1111111×1.1111111 = 1.23456787654321",
    answer: 1.23456787654321,
    type: "巧算技巧-规律探究",
    source: "5-1.md 奥赛难度 - 长循环对称数规律"
  }
];